Gravitational funnel

Description

In a funnel with an hyperbolic vertical section and a smooth internal side, we make a small steel sphere slide freely.

If you launch the sphere horizontally (Clip A), it spins describing an almost perfectly circular orbit, slowly spiraling down; you can easily notice how the speed increases as the sphere goes down towards the bottom of the funnel. Seen from above, the motion of the sphere is similar to that of a meteor caught by a gravitational attraction of a planet.

Clip A

If the sphere is launched sideways instead (Clip B), then the resulting orbit is elliptic (in the end also in this case, the sphere will fall down into the funnel). In this second case, the motion observed from above shows some similarity with that of a planet around the sun: the trajectory is elliptic (the funnel axis corresponds to one focus of the ellipse, just as the sun does); moreover the speed increases as the sphere approaches the axis, exactly as the earth speed gets higher when our planet gets nearer to the sun.